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Resolución de integrales/ tg^2x/ dx/(tg^2x+1)

Integral de dx/(tg^2x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2               
  /               
 |                
 |       1        
 |  ----------- dx
 |     2          
 |  tan (x) + 1   
 |                
/                 
1
$$\int\limits_{1}^{2} \frac{1}{\tan^{2}{\left(x \right)} + 1}\, dx$$ 
Integral(1/(tan(x)^2 + 1), (x, 1, 2))
Respuesta (Indefinida) [src] 
  /                                                                  
 |                                                             2     
 |      1                     x             tan(x)        x*tan (x)  
 | ----------- dx = C + ------------- + ------------- + -------------
 |    2                          2               2               2   
 | tan (x) + 1          2 + 2*tan (x)   2 + 2*tan (x)   2 + 2*tan (x)
 |                                                                   
/
$$\int \frac{1}{\tan^{2}{\left(x \right)} + 1}\, dx = C + \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} + \frac{x}{2 \tan^{2}{\left(x \right)} + 2} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                                                        2                                2     
        1               2             tan(2)         tan (1)          tan(1)        2*tan (2)  
- ------------- + ------------- + ------------- - ------------- - ------------- + -------------
           2               2               2               2               2               2   
  2 + 2*tan (1)   2 + 2*tan (2)   2 + 2*tan (2)   2 + 2*tan (1)   2 + 2*tan (1)   2 + 2*tan (2)
$$- \frac{\tan^{2}{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} - \frac{\tan{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan{\left(2 \right)}}{2 + 2 \tan^{2}{\left(2 \right)}} - \frac{1}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{2}{2 + 2 \tan^{2}{\left(2 \right)}} + \frac{2 \tan^{2}{\left(2 \right)}}{2 + 2 \tan^{2}{\left(2 \right)}}$$ 
=
= 
                                                        2                                2     
        1               2             tan(2)         tan (1)          tan(1)        2*tan (2)  
- ------------- + ------------- + ------------- - ------------- - ------------- + -------------
           2               2               2               2               2               2   
  2 + 2*tan (1)   2 + 2*tan (2)   2 + 2*tan (2)   2 + 2*tan (1)   2 + 2*tan (1)   2 + 2*tan (2)
$$- \frac{\tan^{2}{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} - \frac{\tan{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan{\left(2 \right)}}{2 + 2 \tan^{2}{\left(2 \right)}} - \frac{1}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{2}{2 + 2 \tan^{2}{\left(2 \right)}} + \frac{2 \tan^{2}{\left(2 \right)}}{2 + 2 \tan^{2}{\left(2 \right)}}$$ 
-1/(2 + 2*tan(1)^2) + 2/(2 + 2*tan(2)^2) + tan(2)/(2 + 2*tan(2)^2) - tan(1)^2/(2 + 2*tan(1)^2) - tan(1)/(2 + 2*tan(1)^2) + 2*tan(2)^2/(2 + 2*tan(2)^2)
Respuesta numérica [src] 
0.0834750194665975
0.0834750194665975

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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